The folding chair has different settings that change the angles formed by its parts. Suppose mangle2 is 31 and mangle3 is 72. Find mangle1. The diagram is not to scale.
The image of a quadrilateral and its extended sides and diagonals is shown to resemble a folding chair.
· The left side of the quadrilateral is extended up to form the back of the folding chair.
· The top side of the quadrilateral is extended to the right to form the arm rest of the folding chair.
· The right side of the quadrilateral is extended down to form the front leg of the folding chair.
· The diagonal between the upper right vertex of the quadrilateral and the lower left vertex is extended towards the left to form the back leg of the folding chair.
· Angle 1 is formed by the extended left side and the top side of the quadrilateral so that angle 1 is outside of the quadrilateral.
· Two angles are created by the diagonal.
· Angle 2 is formed by the diagonal and the top side of the quadrilateral.
· Angle 3 is formed by the diagonal and the left side of the quadrilateral.
(1 point)
Responses
a.123
b.113
c. 93
d. 103
To find mangle1, we need to use the fact that the sum of the angles in a quadrilateral is equal to 360 degrees.
First, let's find the measure of angle 4 (the angle at the upper right vertex of the quadrilateral).
Since mangle2 is given as 31 degrees and mangle3 is given as 72 degrees, we can use the fact that opposite angles are congruent to find the measure of angle 4.
Since angle 2 and angle 3 are opposite angles, they must be congruent.
So, mangle2 = mangle3 = angle 4 = 72 degrees.
Now, we can use the fact that the sum of the angles in a quadrilateral is equal to 360 degrees to find mangle1.
360 = angle 1 + angle 2 + angle 3 + angle 4
360 = angle 1 + 31 + 72 + 72
360 = angle 1 + 175
Subtracting 175 from both sides:
185 = angle 1
Therefore, mangle1 is equal to 185 degrees.
Therefore, the correct answer is:
d. 103
To find mangle1, let's apply the Angle Sum Property of a Quadrilateral, which states that the sum of the angles in a quadrilateral is equal to 360 degrees.
Since mangle2 and mangle3 are given, we can find the measures of the other two angles:
mangle2 = angle2 = 31 degrees
mangle3 = angle3 = 72 degrees
Using the Angle Sum Property, we can set up the equation:
mangle1 + mangle2 + mangle3 + angle4 = 360 degrees
We know that angle4 is formed by the extended right side and the extended diagonal. Since the sum of the interior angles of a triangle is 180 degrees, we have:
angle4 = 180 degrees - angle2 - angle3
= 180 degrees - 31 degrees - 72 degrees
= 77 degrees
Now, substituting the known values into the equation:
mangle1 + 31 degrees + 72 degrees + 77 degrees = 360 degrees
mangle1 + 180 degrees = 360 degrees
Subtracting 180 degrees from both sides:
mangle1 = 360 degrees - 180 degrees
= 180 degrees.
Therefore, mangle1 is 180 degrees.
The correct answer is:
a. 123